Question

14.
If the equation, sin’x - a sin x+b=0 has only one solution n (0,r) then which of the
following statements are correct.
a) a € (-0,1] [2,00)
b) b=(-0,0] [1,00)
c) a =1+b
d) none of these​

Answer 1

Answer:

sin

2

x−asinx+b=0 has only one solution in (0,π).

⇒ sinx=1 gives one solution and sinx=α gives other solution such that α>1 or α≤0

⇒ (sinx−1)(sinx−α)=0 is the same equation as sin

2

x−asinx+b=0

⇒ 1+α=a and α=b

⇒ 1+b=a and b>1 or b≤0

⇒ bϵ(−∞,0]∪[1,∞) and aϵ(−∞,1]∪[2,∞)